An Unusual Accident

RAY: This puzzler was sent in by Mark Sackler. He writes, "This really happened to me many years ago, in 1984, to be precise. Here are all the facts.

"My 1982 Toyota Celica rear-ended another vehicle. The other vehicle was stationary at the instant of the accident. My car was unoccupied at the time of the accident. I was a passenger in the other vehicle when it was struck my car. And the accident was the other vehicle's fault and their insurance paid for the damage to my vehicle."